Energy Detectors and Asymptotic Symmetries

TL;DR

This paper explores energy detector operators at null infinity in gauge theories and gravity, revealing their conformal primary nature, universal OPE structure, and connection to soft charges and symmetries in celestial holography.

Contribution

It introduces a new class of energy detectors as conformal primaries, derives their OPE structure, and links particle counting to soft currents in celestial holography.

Findings

Energy detectors transform as conformal primaries on the celestial sphere.

Universal leading structure of the operator product expansion is derived.

Particle number operators are expressed as products of soft currents in gravity and gauge theories.

Abstract

We study detector operators measuring energy to a power $\Delta-2$ at null infinity in four-dimensional gauge theories and gravity. These operators transform as conformal primaries on the celestial sphere and provide a natural basis for describing energy-flux observables in scattering processes. Using the collinear factorization of scattering amplitudes, we derive the universal leading structure of the operator product expansion. A key consequence of our analysis is the precise identification of the $\Delta=2$ detector, the number operator. Exploiting the fact that soft charges generate symmetries of the S-matrix, we demonstrate that the number of particles is entirely determined by the product of two soft currents: in gravity, the operator is the square of the supertranslation generator, while in Yang-Mills yields a product of $SU(N)$ Kac-Moody soft currents. This work establishes thus a direct link between detector observables and the soft sector of celestial holography.